Applications of a General Stable Law Regression Model

Abstract

In this paper we present a method for performing regression with stable disturbances. The method of maximum likelihood is used to estimate both distribution and regression parameters. Our approach utilises a numerical integration procedure to calculate the stable density, followed by sequential quadratic programming optimisation procedures to obtain estimates and standard errors. A theoretical justification for the use of stable law regression is given followed by two real world practical examples of the method. First, we fit the stable law multiple regression model to housing price data and examine how the results differ from normal linear regression. Second, we calculate the beta coefficients for 26 companies from the Financial Times Ordinary Shares Index.